Principles of Inventory Management: When You Are Down to Four, Order More

352 Pages·2010·3.2 MB·English

by  John A. Muckstadt

Springer Series in Operations Research
And Financial Engineering

Series Editors:
Thomas V. Mikosch
Sidney I. Resnick
Stephen M. Robinson

F orothertitlespublishedinthisseries,goto
h ttp://www.springer.com/series/3182
John A. Muckstadt
Amar Sapra

Principles of Inventory
Management

When You Are Down to Four, Order More

123
John A. Muckstadt Amar Sapra
School of Operations Research Department of Quantitative Methods
and Information Engineering and Information Systems
Cornell University Indian Institute of Management
286 Rhodes Hall Bangalore
Ithaca, NY 14853-3801 Bannerghatta Road
USA Bangalore 560 076
[email protected] Indi a
[email protected]

Series Editors:
Thomas V. Mikosch Stephen M. Robinson
Department of Mathematical Sciences Department of Industrial and Systems Engineering
University of Copenhagen University of Wisconsin-Madison
DK-1017 Copenhagen Madision, WI 53706
Denmark USA
[email protected] [email protected]

Sidney I. Resnick
Cornell University
School of Operations Research and
Information Engineering
Ithaca, NY 14853
USA
[email protected]

ISSN 1431-8598
ISBN 978-0-387-24492-1 e-ISBN 978-0-387-68948-7
DOI 10.1007/978-0-387-68948-7
Springer New York Dordrecht Heidelberg London

Library of Congress Control Number: 2009939430

Mathematics Subject Classification (2010): 90-01, 90B05, 90C39

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To mywife, Linda,myparents,mychildren,and
grandchildren,who havesupportedandinspiredme.
—JackMuckstadt
To myparentsandsiblingsfortheir continuedsupport
andencouragement.Myparentshavelived adifficult
lifeandhavedenied themselvesmost pleasuresinlife
justtomakesurethattheirchildrenwereabletoobtain
thebestpossibleeducation.
—AmarSapra
Preface
The importance of managing inventories properly in global supply chains cannot be
denied. Eachcomponent ofthese numerous supply chains mustfunction appropriately
so that inventories are managed efficiently. To manage efficiently requires the leaders
and staffs in each organization to comprehend certain basic principles and laws. The
purpose ofthisbookistodiscuss theseprinciples.
Thecontentsofthistextrepresentacollectionoflecturenotesthathavebeencreated
overthepast33yearsatCornellUniversity.Assuch,thetopicsdiscussed,thesequence
in which they are presented, and the level of mathematical sophistication required to
understand the contents of this text are based on my interests and the backgrounds of
mystudents. Clearly, notalltopics found inthe vastliterature onquantitative methods
used to model and solve inventory management problems can be covered in a one-
semestercourse. Consequently, thisbookislimitedinscopeanddepth.
Thecontentsofthebookareorganized inamannerthatIhavefoundtobeeffective
in teaching the subject matter. After an introductory chapter inwhich the fundamental
issues pertaining to the management of inventories are discussed, we introduce a vari-
ety of models and algorithms. Each such model is developed on the basis of a set of
assumptions aboutthemannerinwhichanoperating environment functions.
In Chapter 2 we study the classic economic order quantity problem. This type of
problem isbased onthe assumption that demands occur ataconstant, continuous, and
known rate over an infinite planning horizon. Furthermore, the cost structure remains
constant over this infinite horizon as well. The focus is on managing inventories at a
singlelocation.
The material in Chapter 3 extends the topic covered in Chapter 2. Several multi-
locationormulti-itemmodelsareanalyzed.Theseanalysesarebasedonwhatarecalled
power-of-twopolicies. Again,theunderlying operatingenvironments areassuredtobe
deterministic andunchanging overaninfinitehorizon.
vii
viii Preface
The assumptions made about the operating environment are altered in Chapter 4.
Here the planning horizon is finite in length and divided into periods. Demands and
costs are assumed to be known in each period, although they may change from period
toperiod.
In all subsequent chapters, uncertainty is present in the operating environment. In
Chapter 5 we study single-period problems in which customer demand is assumed to
be described by a random variable. In Chapter 6, the analysis is extended to multiple
periods.Thediscussionlargelyfocusesonestablishingpropertiesofoptimalpoliciesin
finite-horizon settings when demand is described by a non-stationary process through
time.Serialsystemsarealsodiscussed. Theobjectiveistominimizetheexpectedcosts
ofholdinginventoriesandstockingout.Thus,thecoststructureinthischapterislimited
tothecasewheretherearenofixedordering costs.
In Chapter 7, we study environments in which demands can occur at any point in
time over an infinite planning horizon. Whereas we assumed in Chapter 6 that inven-
tory procurement decisions were made periodically, in this chapter we assume such
decisions are made continuously in time. The underlying stochastic processes govern-
ing the demand processes are stationary over the infinite planning horizon, as are the
costs.AsinChapter6,weassumetherearenofixedordering costs.
The analysis in Chapter 7 is confined to managing items in a single location. In
Chapter 8 we extend the analysis to multi-echelon systems. Thus the underlying sys-
tem is one in which inventory decisions are made continuously through time, but now
in multiple locations. The importance of understanding the interactions of inventory
policies betweenechelons isthemaintopicofthischapter.
Chapters 9 and 10 contain extensions of the materials in Chapters 7 and 6, respec-
tively. In both chapters, we introduce the impact that fixed ordering costs have on the
form of optimal operating policies as well as on the methods used to model and solve
theresultingoptimization problems. Bothexactandapproximate modelsarepresented
alongwithappropriatealgorithmsandheuristics.Aproofoftheoptimalityofso-called
(s,S)policies isgiven,too.
Asmentioned, thematerials contained inthis text areones that have been taught to
Cornell students. These students are seniors and first year graduate students. As such,
they have studied optimization methods, probability theory (non-measure-theoretic)
and stochastic processes in undergraduate level courses prior to taking the inventory
management course. In addition to presenting fundamental principles to them, the in-
tent ofthe course isalsotodemonstrate theapplication ofthetopics they havestudied
previously.
The text is written so that sections can be read mostly independently. To make this
possible, notation ispresented ineachmajorsection ofeachchapter. Thetextcouldbe
used in different ways. For example, a half semester course could consist of material
in Chapter 2, Section 4.1, Sections 5.1–5.2, Sections 6.2–6.3, most of Sections 9.1–
Preface ix
9.2,Sections10.1–10.2,andSection10.5.Whilewehavechosentoexaminestochastic
lot sizing problems at the end of the text, these materials could easily be studied in
a different sequence. For example, Chapter 9 could be studied after Chapter 3, and
Chapter 10 could be studied after Chapter 6. Rearranging the sequence in which the
textcanbereadispossiblebecause ofthewayithasbeenwritten.
I have mentioned that the scope of this text is limited. I encourage readers to study
other textstocomplete their understanding ofthebasic principles underlying thetopic
of inventory management. These texts include those authored by Sven Axsa¨ter; Ed
Silver and Rein Peterson; Steve Nahmias; Craig Sherbrooke; Paul Zipkin; and Evan
Porteus. Each of these authors has made exceptional contributions to the science and
practiceofinventory management.
Ithaca, NY JohnA.Muckstadt
May2009
Acknowledgments
I began my study of inventories while a student at the University of Michigan. My
teachers there, Richard C. Wilson and Herbert P. Galliher, taught me the basics of the
subject. These two were great teachers and engineers. They prodded and encouraged
meduringandaftermystudentyears. Iamdeeplyindebtedtothem.
As is often the case in a person’s life, an event occurred that altered every profes-
sional activity I have undertaken thereafter. This event occurred for me in the early
1970s when I was asked to develop an approach for computing procurement quanti-
ties for engines and other repairable items for the U.S. Air Force’s F-15 aircraft. At
that time I was an active duty Air Force Officer. Suddenly, I had to truly learn and
then apply the principles of inventory theory. The people with whom I worked on this
projectwerecapable,dedicated, andtrulyofgreatcharacter.AttheAirForceLogistics
CommandHeadquarters,whereIworked,thesepeopleincludedMajorGeneralGeorge
Rhodes,ColonelFredGluck,MajorGenePerkins,CaptainJonReynolds,CaptainMike
Pearson, MSgt Robert Kinsey, Tom Harruff, Vic Presutti, and Perry Stewart. I learned
much from my friends and colleagues at the RAND Corporation: Irv Cohen, Gordon
Crawford, Steve Drezner, Murray Geisler, Jack Abel, Mort Berman, Lou Miller, Bob
Paulson, Hy Shulman, and John Lu. I also benefited greatly from research conducted
at RAND by Craig Sherbrooke. Many of the ideas presented in Chapter 8 are directly
related tohisefforts. Also, Ihad thedistinct privilege oflearning about thepractice of
inventory management from Bernie Rosenman, who headed the Army Inventory Re-
searchOffice,andhiscolleagues KarlKruseandAlanKaplan.
Since 1974 I have been on the faculty at Cornell and have had the opportunity to
work with some of the finest scholars in the field of operations research. Peter Jack-
son, Bill Maxwell, Paat Rusmevichientong, and Robin Roundy all have greatly influ-
enced my thinking about the principles of inventory management. I have been fortu-
natetohavetaughtandworkedwithmanygiftedstudents. Almost1,000students have
xi
xii Acknowledgments
been taught inventory management principles at Cornell since 1974. I am especially
indebted to many former Ph.D. students, who, without exception, have been wonder-
ful people and a great joy to work with. They include Kripa Shanker, Peter Knepell,
Mike Isaac, Jim Rappold, Kathryn Caggiano, Andy Loerch, Bob Sheldon, Ed Chan,
Alan Bowman, David Murray, Jong Chow, Eleftherios Iacovou, Susan Alten, Chuck
Sox, Howard Singer, Sophia Wang, Juan Pereira, and, most recently, Retsef Levi, Tim
Huh, and Ganesh Janakiraman. Major sections of Chapter 10 are due to these latter
three. Thanks also to Tim Huh, Retsef Levi, Ganesh Janakiraman, and Joseph Geunes
fortheirearlyadoptionofthebookandhelpful feedback.
AmarSapra, myco-author and formerCornell student, urged mefor manyyears to
writethisbook.Withouthisencouragement andsubstantial assistance, thebookwould
nothavebeencompleted.
IcannotexpresswithmerewordshowthankfulIamtoallofthesetrulyexceptional
people.
I also appreciate the heroic efforts of June Meyermann, who had to decipher my
handwriting as she typed the manuscript. Sheis ajewel. Kathleen King and PaatRus-
mevichientong have provided substantial support in the preparation of this book, as
well.
Lastly, and most importantly, my wife Linda has been very supportive of the time
I have spent working on the text. The many hours that I have not been available for
activities withheraretoonumeroustocount.Ideeplyappreciate herconstantloveand
support.